Resarchs on Solutions of Nonlinear Elliptic Equations and Numcrical Analysis

非线性椭圆方程解及数值分析研究

基本信息

批准号：
09440087
负责人：
YOTSUTANI Shoji
金额：
$ 3.14万
依托单位：
Ryukoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

Head investigator S.Yotsutani proposed a very accurate numerical computation method to solve Poisson's equation by using a charge simulation method with H.Morishita, N.Kobayashi, H.Takaichi and K.Amano. Recently, He has succeeded to shorten the time of the calculation considerably and improve the accuracy with H.Morishita and K.Anjano, This method is in the conformity with the paerallel computing. Thus it is possible to know the detailed shape of solutions of nonlinear elliptic systems.On the other hand, he developed the mathematical method of investigate the shape of radially symmetric solutions with Y.Kabeya and E.Yanagida. Recently, he has found the systematic change of variables to transform the differential equations arising from the elliptic equations to canonical form with E.Yanagida. Thus, relations between various equations studied one by one independently become very clear, and the understandings encourage the deep understanding of the propertites of each solution.The reserach results of investigators are asfollows. T.lkeda invesitigate the instabiliz ation of the standing pulse solutions of bistable reaction-diffusion systems. Y.Morita showed stabilization of vorticies in the Ginzburg-Landau equation with a variable diffusion coefficient. H.Oka investigated the connecting orbit structure of monotone solutions in the shadow system. Y.Yamada proved the coexistence states for some population models with nonlinear cross-diffusion. E.Yanagida discoverd various new phenomena of the systems of parabolic equations and gave the proof of them.

负责人S. yotsutani提出了一种非常准确的数值计算方法，通过使用H.Morishita，N.Kobayashi，H.Takaichi和K.Amano使用电荷仿真方法来求解Poisson的方程。最近，他成功地缩短了计算时间，并提高了H. -Morishita和K.anjano的准确性，此方法与PAERALALL PAREALLALL COMPUTING相符。因此，可以知道非线性椭圆系统的详细溶液形状。另一方面，他开发了使用Y.Kabeya和e.yanagida研究径向对称溶液的形状的数学方法。最近，他发现了变量的系统变化，以转化从椭圆形方程引起的微分方程，并使用e.yanagida转变为规范形式。因此，一个独立研究的各种方程之间的关系变得非常清晰，并且理解鼓励对每个解决方案的性质有深刻的理解。研究人员的回归结果是遵循的。 T.Lkeda侵入了Bistable Reaction-扩散系统的常规脉冲解决方案的Instabiliz。 Y.morita显示出具有可变扩散系数的金茨堡 - 兰道方程中涡度的稳定。 H.Oka研究了阴影系统中单调溶液的连接轨道结构。 Y.Yamada证明了某些具有非线性交叉扩散的人群模型的共存状态。 E.Yanagida发现了抛物线方程系统的各种新现象，并给出了它们的证明。